CPA Bar Quiz: Apply Valuation Models

What this quiz covers

This quiz focuses on Apply Valuation Models, giving you a quick way to practice the rules, question types, and explanations that matter most for CPA Bar.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $948.60 (correct answer)
2. $1,000.00
3. $1,051.40
4. $972.00

Explanation: Annual coupon = $1,000 x 6% = $60. PV of coupons = $60 x 2.577 = $154.62. PV of face value = $1,000 x 0.794 = $794.00. Bond price = $154.62 + $794.00 = $948.62, approximately $948.60. When market yield exceeds coupon rate, bonds trade at a discount to face value. Option B is face value, which applies only when coupon rate equals market yield. Option C is a premium price, which would apply if the coupon rate exceeded the market yield. Option D applies an incorrect annuity factor.

Question 2

1. $30.00
2. $75.00
3. $52.00 (correct answer)
4. $60.00

Explanation: Gordon Growth Model: P = D1 / (r - g). D1 = D0 x (1 + g) = $3.00 x 1.04 = $3.12. P = $3.12 / (0.10 - 0.04) = $3.12 / 0.06 = $52.00. Option A divides only D0 by the required rate of return, omitting the growth rate. Option B divides D1 by only the growth rate. Option D uses D0 in the numerator without the growth adjustment.

Question 3

1. $40,000
2. $5,000
3. $50,000
4. $62,500 (correct answer)

Explanation: PV of perpetuity = Annual payment / Discount rate = $5,000 / 0.08 = $62,500. Option A divides by 0.125 (a different rate). Option B reports the annual payment rather than the present value. Option C uses a 10% discount rate instead of 8%.

Question 4

1. $319,440
2. $200,000
3. $239,580 (correct answer)
4. $299,250

Explanation: After-tax annual lease payment = $80,000 x (1 - 0.25) = $60,000. PV of after-tax lease payments = $60,000 x 3.993 = $239,580. Option A applies the pre-tax lease payment to the annuity factor without the tax reduction. Option B multiplies the after-tax payment by 5 years without discounting. Option D applies the pre-tax payment and an incorrect annuity factor.

Question 5

1. $2,300,000
2. $4,200,000
3. $5,000,000
4. $3,100,000 (correct answer)

Explanation: Adjusted total assets = Book value + Unrecorded intangibles = $4,200,000 + $800,000 = $5,000,000. Equity value = Adjusted assets - Liabilities = $5,000,000 - $1,900,000 = $3,100,000. Option A uses only book value assets minus liabilities, omitting the unrecorded intangibles. Option B reports only the book value of assets. Option C reports the adjusted asset total before subtracting liabilities.

Question 6

1. The 12% growth assumption is acceptable if senior management endorses it
2. Acquisitions always generate synergies that justify assuming higher growth than historical rates
3. The model should be rerun using the 8% midpoint between historical and assumed growth
4. The acquisition's value depends on achieving three times the historical growth rate; sensitivity analysis should test whether value is preserved at growth rates closer to the historical baseline (correct answer)

Explanation: When an acquisition requires a substantial departure from historical performance to produce a positive NPV, the investment is highly sensitive to that assumption. Sensitivity and scenario analysis - testing NPV at historical growth (4%), a moderate improvement (8%), and the full assumption (12%) - reveals the range of outcomes and the probability that the deal creates value. Management endorsement does not make an aggressive assumption reliable, and synergies do not automatically triple a company's growth rate. Option C introduces an arbitrary midpoint without analytical justification. Option B is an unsupported generalization.

Question 7

1. Project C should be rejected because a 6-year payback period always signals excessive risk
2. Selecting Project D over Project C sacrifices $85,000 of shareholder value; the payback period ignores cash flows beyond the recovery point and does not account for the time value of money (correct answer)
3. The payback period is more reliable than NPV for projects with long time horizons
4. Both projects should be accepted because both generate positive NPV and capital is unconstrained

Explanation: The payback period ignores all cash flows after the investment is recovered and does not discount future cash flows. A project with a long payback but high NPV may generate most of its value after the payback point. Overweighting payback leads to rejecting long-horizon, high-value projects in favor of faster-recovering, lower-value alternatives - exactly the tradeoff here. Option A makes an absolute rule about payback length that has no analytical basis. Option C inverts the well-established ranking of decision criteria. Option D is incorrect because the projects are implicitly mutually exclusive given that management is choosing between them.

Question 8

1. 10.0%
2. 7.2%
3. 9.6%
4. 11.2% (correct answer)

Explanation: CAPM: Cost of equity = Risk-free rate + (Beta x Equity risk premium) = 4% + (1.2 x 6%) = 4% + 7.2% = 11.2%. Option A omits the beta adjustment and uses the raw risk-free rate plus equity risk premium without beta. Option B reports only the beta-adjusted risk premium without adding the risk-free rate. Option C uses a beta of 1.0 rather than 1.2.

Question 9

1. Unconventional cash flows always produce an IRR above WACC, so the project should be rejected
2. The second analyst is incorrect; IRR is always a reliable measure regardless of cash flow patterns
3. The payback period should be used instead of IRR for all capital projects
4. Projects with unconventional cash flows may yield multiple IRRs or no real IRR, making the standard accept-or-reject IRR rule unreliable; NPV is the more appropriate evaluation method (correct answer)

Explanation: IRR assumes that all cash flows - both inflows and outflows - follow a single sign change (negative then positive). When cash flows change sign more than once (positive, then negative, then positive again), the IRR calculation may produce multiple mathematically valid solutions or no real solution. Using one of these multiple IRRs to compare against WACC produces an unreliable decision signal. NPV does not have this limitation and remains valid for unconventional cash flow patterns. Option A draws an incorrect general conclusion. Option B dismisses a well-documented limitation. Option C overgeneralizes from one limitation of IRR.

Question 10

1. 8.52% (correct answer)
2. 7.85%
3. 9.20%
4. 10.00%

Explanation: After-tax cost of debt = 6% x (1 - 0.25) = 4.5%. Weight of equity = $600,000 / $1,000,000 = 60%. Weight of debt = 40%. WACC = (60% x 11.2%) + (40% x 4.5%) = 6.72% + 1.80% = 8.52%. Option B applies an incorrect weighting or cost of equity. Option C uses the pre-tax cost of debt rather than the after-tax cost. Option D applies equal weights or ignores the tax shield.

Question 11

1. $50,000
2. $200,000
3. $9,720 (correct answer)
4. -$9,720

Explanation: PV of annuity = $40,000 x 3.993 = $159,720. NPV = $159,720 - $150,000 = $9,720. Option A subtracts the annual cash flow from the initial investment rather than computing PV. Option B reports the total undiscounted cash flows ($40,000 x 5 = $200,000). Option D applies the correct formula but labels the sign incorrectly.

Question 12

1. Project A, because its higher IRR of 18% indicates a higher percentage return on invested capital
2. Project B, because it creates more absolute value for shareholders at $75,000 versus $50,000, and both projects exceed the cost of capital (correct answer)
3. Either project is acceptable because both produce positive NPV and IRR above the cost of capital
4. Project A, because IRR is always the superior decision criterion for mutually exclusive projects

Explanation: For mutually exclusive projects, NPV is the preferred decision criterion because it measures the absolute dollar value created for shareholders. Project B's NPV of $75,000 exceeds Project A's $50,000, meaning Project B creates $25,000 more value. The IRR conflict arises because the projects likely differ in scale or timing - Project B may require a larger investment but generates more total value. Option A elevates IRR over NPV, which is the classic error in mutually exclusive project analysis. Option C is incorrect; when projects are mutually exclusive, only one can be chosen. Option D is a general overstatement about IRR's superiority.

Question 13

1. -$6,590
2. $6,590 (correct answer)
3. $60,000
4. $206,590

Explanation: PV of cash flows: ($60,000 x 0.909) + ($70,000 x 0.826) + ($80,000 x 0.751) + ($50,000 x 0.683) = $54,540 + $57,820 + $60,080 + $34,150 = $206,590. NPV = $206,590 - $200,000 = $6,590. Option A applies the correct calculation but labels the sign incorrectly. Option C reports only Year 1 cash flows. Option D reports the total present value without subtracting the initial investment.

Question 14

1. The discount rate that maximizes the net present value of a project's cash flows
2. The discount rate at which the net present value of a project equals zero (correct answer)
3. The average annual return expressed as a percentage of the original investment cost
4. The minimum required rate of return established by management for approving capital investments

Explanation: The IRR is the specific discount rate that sets NPV equal to zero - the rate at which the present value of future cash inflows exactly equals the initial investment. A project is accepted when its IRR exceeds the required rate of return. Option A is incorrect; higher discount rates reduce NPV rather than maximizing it. Option C describes the accounting rate of return. Option D describes the hurdle rate or cost of capital, which is used as the acceptance benchmark for IRR, not the definition of IRR itself.

Question 15

1. Discounting expected future cash flows or earnings at a rate reflecting the risk of those cash flows (correct answer)
2. Summing the fair values of all identifiable assets and subtracting the fair values of all liabilities
3. Applying a valuation multiple derived from prices paid in recent comparable company transactions
4. Calculating the replacement cost of the assets required to replicate the company's operations

Explanation: The income approach estimates value by converting future economic benefits into a present value using an appropriate discount rate. Common income approach methods include DCF analysis and the capitalization of earnings. Option B describes the asset (or cost) approach, which values a business by reference to the net asset value. Option C describes the market approach using precedent transactions. Option D describes the replacement cost variant of the asset approach.

Question 16

1. Discounting all expected future cash flows to their present value and comparing the total to the initial investment outlay (correct answer)
2. Calculating the number of years required for cumulative undiscounted cash flows to recover the initial investment
3. Determining the discount rate at which the present value of future cash flows equals the initial investment
4. Dividing average annual accounting income by the average book value of the investment over its life

Explanation: NPV discounts each expected future cash flow back to the present using the required rate of return, sums those present values, and subtracts the initial investment. A positive NPV indicates the investment creates value above the cost of capital. Option B describes the payback period. Option C describes the internal rate of return (IRR). Option D describes the accounting rate of return.

Question 17

1. 2.4 years (correct answer)
2. 2.0 years
3. 3.0 years
4. 2.7 years

Explanation: Cumulative cash flows: End of Year 1 $120,000; End of Year 2 $260,000; remaining to recover = $300,000 - $260,000 = $40,000. Year 3 cash flow = $100,000. Fraction of Year 3 = $40,000 / $100,000 = 0.40. Payback = 2 + 0.40 = 2.4 years. Option B assumes the Year 2 cumulative total recovers the full investment. Option C assumes the investment is not recovered until the end of Year 3. Option D applies an incorrect fraction of the Year 3 cash flow.

Question 18

1. Average the two values to arrive at $49,000,000 as the offer price
2. Discard the comparable company analysis because market multiples are inherently more subjective than DCF
3. Investigate the assumptions driving the gap, since DCF value depends on growth and discount rate assumptions while comparable company multiples reflect what the market currently pays for similar businesses (correct answer)
4. Use the lower DCF value as a conservative floor and proceed with that as the maximum offer

Explanation: A significant gap between DCF and market multiple valuations usually signals that one or both methodologies contain assumptions worth scrutinizing. DCF is highly sensitive to terminal growth rate and discount rate inputs, while comparable company multiples may include a market-specific control premium or reflect current sector optimism. Understanding why the gap exists is more informative than arbitrarily averaging or discarding a method. Option A treats two different analytical conclusions as though they should be mechanically blended. Option B incorrectly dismisses market-based evidence. Option D accepts the lower value without understanding why the two methods diverge.

Question 19

1. The precedent transaction multiple is more accurate because it reflects actual market prices
2. The DCF model should be adjusted upward to match the transaction multiple
3. The gap may reflect control premiums embedded in transaction prices or conservative DCF assumptions; both warrant scrutiny before reaching a valuation conclusion (correct answer)
4. The firm should use only DCF and disregard transaction market data

Explanation: A higher multiple in precedent transactions versus DCF is common for several reasons: transaction prices include control premiums paid by acquirers, market sentiment at the time of transactions may differ from current conditions, and DCF assumptions may be overly conservative (high discount rate or low growth assumption). Both signals are informative and neither should be dismissed outright. The analyst should examine whether the DCF assumptions are realistic and whether the transaction sample is comparable before concluding on value. Options A, B, and D each arbitrarily elevate one method over the other without analytical basis.

Question 20

1. The stock is overvalued and should be sold immediately based on the model output
2. The Gordon Growth Model is always correct and the market price must be wrong
3. The gap may indicate the market is pricing in higher future growth or a lower required return than the model assumed; the analyst should evaluate whether the model inputs are realistic before drawing a conclusion (correct answer)
4. Model-based valuations are irrelevant for publicly traded companies because markets are always efficient

Explanation: A model value below the market price does not automatically mean the stock is overvalued. The Gordon Growth Model is highly sensitive to the growth rate (g) and required return (r) inputs - small changes in these assumptions produce large changes in estimated value. The market price may reflect a more optimistic growth outlook, a different perception of risk, or factors the model does not capture. Before concluding the stock is overvalued, the analyst should stress-test the model assumptions and determine whether they are more or less realistic than what the market implies. Options A and B reach premature conclusions without examining model inputs. Option D is an overstated version of the efficient market hypothesis that dismisses analytical tools entirely.